26:48
Oxford CountDown level 5 Solution Exercise 2a Complete
Maths CR
Overview
This video explains the concepts of multiples and factors, focusing on divisibility rules. It begins with a crossword activity to reinforce these terms and then delves into the rules for divisibility by 2, 3, 4, 5, 6, 8, 9, and 10. The latter half of the video applies these rules to solve various exercises, including identifying numbers divisible by specific factors, determining true or false statements about divisibility, and selecting correct answers from multiple-choice options. The emphasis is on understanding and applying these rules for mathematical problem-solving.
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Chapters
- The unit introduces the concepts of multiples and factors.
- A crossword activity is used to review and reinforce understanding of factors and multiples.
- Clues in the crossword define terms like multiples (e.g., numbers that result from multiplying a base number by integers) and factors (numbers that divide another number evenly).
- Prime numbers are defined as numbers with exactly two factors: 1 and themselves.
Understanding multiples and factors is foundational for arithmetic operations and number theory, enabling deeper comprehension of number relationships.
The clue 'Numbers one, 4, 6, 8, 10, and 12 are dashes of number two' is solved by identifying these as multiples of two.
- Divisibility rules provide shortcuts to determine if a number can be divided by another without a remainder.
- A number ending in 0 is divisible by 5.
- Even numbers are always divisible by 2.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 10 if it ends in 0.
These rules simplify complex division problems, saving time and reducing the chance of calculation errors.
The number 20 is divisible by 5 because it ends in 0; 50 is also divisible by 5 for the same reason.
- A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- A number is divisible by 9 if the sum of its digits is divisible by 9.
Mastering these rules allows for efficient checking of divisibility for larger numbers, crucial for factorization and simplification.
For divisibility by 4, the number 624 is checked by looking at '24', which is divisible by 4, thus making 624 divisible by 4.
- The video presents exercises where learners must identify numbers divisible by specific factors (e.g., 4, 6, 8, 9).
- True/False questions test the understanding of divisibility statements.
- Multiple-choice questions require selecting the correct divisor or property of a number.
- Working through examples involves applying the learned divisibility rules systematically.
Practical application through exercises solidifies understanding and builds confidence in using divisibility rules.
To check if 9482 is divisible by 9, the digits are summed (9+4+8+2=23), and since 23 is not a multiple of 9, the number is not divisible by 9.
- Identifying numbers divisible by 3 but not by 6 requires checking for divisibility by 3 and the absence of divisibility by 2 (i.e., being an odd number).
- Numbers ending in three zeros are divisible by 8, 4, and 10.
- A number divisible by 6 must be an even number.
- The product of two numbers can be checked for divisibility by a third number using the properties of multiplication and divisibility.
These specific scenarios highlight nuanced applications of divisibility rules, preparing learners for more complex mathematical challenges.
The number 477 is divisible by 3 (4+7+7=18) but not by 2 (it's odd), therefore it is divisible by 3 but not by 6.
Key takeaways
- Divisibility rules are shortcuts to determine if a number can be divided evenly by another number without performing the full division.
- Understanding the relationship between divisibility by smaller primes (2 and 3) and divisibility by their product (6) is essential.
- The sum of digits is a key component for divisibility rules of 3 and 9.
- The last digits of a number (one, two, or three) are critical for divisibility rules of 2, 4, 5, 8, and 10.
- Prime numbers have only two factors: 1 and themselves.
- Applying divisibility rules requires systematic checking of the relevant conditions for each rule.
- Numbers ending in 0 or 5 are divisible by 5, while numbers ending in 0 are divisible by 10.
Key terms
MultipleFactorDivisibleRemainderPrime NumberEven NumberSum of DigitsDivisibility RuleCrosswordExercise
Test your understanding
- How can you determine if a number is divisible by 3 without performing division?
- What is the rule for checking if a number is divisible by 4?
- Explain the relationship between divisibility by 2, 3, and 6.
- How do the last three digits of a number help determine its divisibility by 8?
- What defines a prime number, and how does this relate to its factors?